rewrite_changelog.md

Flowchart for cython_stable_sdft Function

Flowchart

graph TD
    A[Start] --> B[Initialize Variables and Allocate Memory]
    B --> C[Check Memory Allocation]
    C --> D[Quantize Feed-Forward Coefficients]
    D --> E[Initialize norm_factor Array]
    E --> F[Apply Filter to Compute Stable SDFT]
    F --> G[Apply Filter Coefficients to Compute y_real and y_imag]
    G --> H[Normalize Output]
    H --> I[Convert Results to NumPy Array]
    I --> J[Free Allocated Memory]
    J --> K[Return Result]

subgraph "Filter Application Loop"
    direction LR
    F --> L[Loop Over Each Sample]
    L --> M[Compute y_real and y_imag]
end

subgraph "Normalization and Conversion"
    direction LR
    H --> N[Loop Over Each Sample for Normalization]
    N --> O[Normalize y_real and y_imag]
    O --> P[Convert to NumPy Array]
end

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Detailed Flowchart Description

1. Start

   • Initialization of the cython_stable_sdft function.

2. Initialize Variables and Allocate Memory

   • Initialize necessary variables such as y_real, y_imag, norm_factor, exp_factor_real, exp_factor_imag, cos_factor, B_real, B_imag, and A.
   • Allocate memory for y_real, y_imag, and norm_factor.

3. Check Memory Allocation

   • Check if memory allocation was successful. If not, raise a MemoryError.

4. Compute Quantized Coefficients

   • Compute and quantize the coefficients for the filter:
     • exp_factor_real and exp_factor_imag for the exponential factor.
     • cos_factor for the cosine factor.
   • Quantize these coefficients to ensure precision.

5. Initialize norm_factor Array

   • Initialize the norm_factor array to 1.0 (simplified normalization).

6. Apply Filter to Compute Stable SDFT

   • Apply the filter to compute the stable SDFT for each sample in the signal:
     • Loop over each sample in the signal:
       • Compute y_real and y_imag for Each Sample
         • For each sample, compute the real part (y_real) and imaginary part (y_imag) of the output using the quantized coefficients and previous samples.
         • Apply feedback using the A coefficients.

7. Normalize Output

   • Normalize the output by dividing y_real and y_imag by the norm_factor.

8. Convert Results to NumPy Array

   • Convert the results (y_real and y_imag) to a NumPy array of complex numbers.

9. Free Allocated Memory

   • Free the allocated memory for y_real, y_imag, and norm_factor.

10. Return Result

    • Return the final result as a NumPy array of complex numbers.